I think I have a solution that will be stronger than the feet but not as pretty. I will put down a 1/4” rubber mat - the type they use at gyms, which is virtually indestructible. This will absorb the irregularities in the tile floor and will be self-leveling.
On top of the mat, I will place composite decking boards, which will distribute the load from the edges of the stand.
I’ll hide it with white trim.
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Self leveling mats will not help.
Key is that you want it to be level, plus have the FORCE on each point be the same.
With a springy mat, sure it will look level, but only because the high points are squished down, which means all the load is still on those
points, which means it twists your stand.
You need shims or adjustable feet.
Lots of shims are great, but a hassle, and they can pop out and move around.
Glad you ordered the feet.